Reconnexion of vortex and magnetic tubes subject to an imposed strain: An approach by perturbation expansion

The viscous interaction of two weakly curved and oppositely directed vortex tubes of flattened cross-section driven together by an imposed uniform strain is considered using a perturbation technique. The evolution of the cross-sectional vorticity distribution is computed, and the rate of reconnexion, as indicated by the decrease of circulation of each tube at the plane of symmetry, is obtained for various values of the Reynolds number and of the (small) aspect ratio of the tubes. Attention is focused particularly on the nonlinear effect of convection by the velocity field induced by the vortices. A similar technique is applied to the problem of reconnexion of magnetic flux tubes, for which the nonlinear effect is different, being that associated with the Lorentz force distribution.